The Evolution of Cataclysmic Variables as Revealed by Their Donor Stars

Abstract

We present an attempt to reconstruct the complete evolutionary path followed by cataclysmic variables (CVs), based on the observed mass-radius relationship of their donor stars. Along the way, we update the semi-empirical CV donor sequence presented previously by one of us, present a comprehensive review of the connection between CV evolution and the secondary stars in these systems, and reexamine most of the commonly used magnetic braking (MB) recipes, finding that even conceptually similar ones can differ greatly in both magnitude and functional form. The great advantage of using donor radii to infer mass-transfer and angular-momentum-loss (AML) rates is that they sample the longest accessible timescales and are most likely to represent the true secular (evolutionary average) rates. We show explicitly that if CVs exhibit long-term mass-transfer-rate fluctuations, as is often assumed, the expected variability timescales are so long that other tracers of the mass-transfer rate-including white dwarf (WD) temperatures-become unreliable. We carefully explore how much of the radius difference between CV donors and models of isolated main-sequence stars may be due to mechanisms other than mass loss. The tidal and rotational deformation of Roche-lobe-filling stars produces 4.5% radius inflation below the period gap and 7.9% above. A comparison of stellar models to mass-radius data for non-interacting stars suggests a real offset of 1.5% for fully convective stars (i.e., donors below the gap) and 4.9% for partially radiative ones (donors above the gap). We also show that donor bloating due to irradiation is probably smaller than, and at most comparable to, these effects. After calibrating our models to account for these issues, we fit self-consistent evolution sequences to our compilation of donor masses and radii. In the standard model of CV evolution, AMLs below the period gap are assumed to be driven solely by gravitational radiation (GR), while AMLs above the gap are usually described by an MB law first suggested by Rappaport et al. We adopt simple scaled versions of these AML recipes and find that these are able to match the data quite well. The optimal scaling factors turn out to be f GR = 2.47 ± 0.22 below the gap and f MB = 0.66 ± 0.05 above (the errors here are purely statistical, and the standard model corresponds to f GR = f MB = 1). This revised model describes the mass-radius data significantly better than the standard model. Some of the most important implications and applications of our results are as follows. (1) The revised evolution sequence yields correct locations for the minimum period and the upper edge of the period gap; the standard sequence does not. (2) The observed spectral types of CV donors are compatible with both standard and revised models. (3) A direct comparison of predicted and observed WD temperatures suggests an even higher value for f GR , but this comparison is sensitive to the assumed mean WD mass and the possible existence of mass-transfer-rate fluctuations. (4) The pred...

Dynamical masses of a nova-like variable on the edge of the period gap

“…Therefore, T eff can be a good tracer of the medium-term (10 3 − 10 5 yr) mass transfer rate (Townsley & Bildsten 2003;Townsley & Gänsicke 2009). The WD effective temperatures predicted by the evolutionary sequences of Knigge et al (2011) are significantly cooler than the data below the period gap, and show a large disagreement in the 3-4 h orbital period range, where the scarce measurements point to much hotter WDs than expected (see fig. 5 of Townsley & Gänsicke 2009 and fig.…”

“…5 of Townsley & Gänsicke 2009 and fig. 16 of Knigge et al 2011). However, the relationship between the time-averaged mass transfer rate and the WD temperature has to be used with caution.…”

“…Another essential observational input to the theory is the time-averaged mass transfer rate, that has to be compared with the predicted secular mass transfer rates (see Knigge, Baraffe & Patterson 2011). A medium-term (10 3 − 10 5 yr) mass transfer rate may be derived from measurements of the effective temperature and mass of the accreting WD (Townsley & Bildsten 2003;Townsley & Gänsicke 2009), which again emphasises the need for accurate binary parameters.…”

Dwarf nova outbursts in intermediate polars

“…by the revised model of Knigge et al (2011) for which the primary mass is 0.7 M . Knigge et al (2011) find that the dispersion of CV properties at a given orbital period is large, which implies that the actual mass transfer rate at a given orbital period may significantly differ from the secular mean, and the dispersion around the black solid line shown in Fig.…”

Spectroscopy From the Hubble Space Telescope Cosmic Origins Spectrograph of the Southern Nova-Like Bb Doradus in an Intermediate State

“…The majority of CVs in our galaxy should have already evolved to a minimum period near 80 minutes and now have degenerate brown dwarf-like secondaries (Howell et al 2001;Goliasch & Nelson 2016). However, some discrepancies have arisen between the observations and the standard model, prompting suggestions of additional (or alternative) theoretical scenarios (see, e.g., Knigge et al 2011 and references therein for a review of the problem).…”